Summary: This study tests two opposing hypotheses about the impact of aid fragmentation on the practice of aid tying. In one, when a small number of donors dominate the aid market in a country, they may exploit their monopoly power by tying more aid to purchases from contractors based in their own countries. Alternatively, when donors have a larger share of the aid market, they may have stronger incentives to maximize the development impact of their aid by tying less of it. Empirical tests strongly and consistently support the latter hypothesis. The key finding -- that higher donor aid shares are associated with less aid tying -- is robust to recipient controls, donor fixed effects and instrumental variables estimation. When recipient countries are grouped by their scores on corruption perception indexes, higher shares of aid are significantly related to lower aid tying only in the less-corrupt sub-sample. This finding is consistent with the argument that aid tying can be an efficient response by donors when losses from corruption may rival or exceed losses from tying aid. When aid tying is more costly, as proxied by donor country size and income, it is less prevalent. Aid tying is lower in the Least Developed Countries, consistent with the OECD Development Assistance Committee's recommendation to its members.